The student body of 3, 191 students has been split up into three categories: Tho

Question

The student body of 3, 191 students has been split up into three categories: Those who prefer the cafeteria food (914), those who prefer the Den food (1075), and those who prefer to cook for themselves (1202). Out of the cafeteria lovers, the probability of them meeting the recommended daily step count of 10, 000 is 30%. Out of the den lovers, the probability of them meeting the recommended daily step is 25%. Out of the chefs, the probability of NOT meeting the step count is 26%. b) I pick a student at random, what is the probability that they prefer the Den and met their steps? Show your work.

Explanation / Answer

Let:
A = prefer the Den

B = meet their steps

So,

P(A) = Number of favourable events/Total number of events = 1075/3191 = 0.3369

Given:
P(B) = 0.25

So,

by Multiplication Theorem of probability:

P(Prefer Den & meet their steps) = P(A) X P(B)

                                               = 0.3369 X 0.25 = 0.0842

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